There are numerous rotary electric shavers, such as for example those marketed by PHILIPS, which utilize a rotary cutter head having a plurality of axially-facing cutting edges. These cutting edges become blunted during long and continual use in shaving, and it is desirable to be able to hone them into a state of adequate sharpness, thereby avoiding cost of unnecessary and too frequent replacement, and avoiding the shaver being out of action for long periods.